MaplePrimes - Newest Questions

Numerical evaluation of a complex integral solution

Paras31 — Mon, 13 Apr 2026 22:44:18 Z

Consider a soil moisture transport problem with parameters: a = 9.88\times10^{-5} m/s, b = -0.0065\ m³/m³, and D = 3.51*10^{-7} m²/s. The length is L=0.08 m, and no-flux (outflow) is assumed, meaning q=0. In this case θ₀= 0.355$ and θL = 0.10.

A solution is expressed as a contour integral involving a complex-valued function V(k,x,t) and evaluated numerically in Maple using parameterized contours k1(r),k2(r),k3(s).

However, when this code is executed, Maple takes an extremely long time and appears to run indefinitely.

Could you suggest an alternative numerical or analytical approach ( that could improve efficiency when evaluating this type of contour integral?

a := 988/10000000;
b := -65/10000;
d := 351/1000000000;
q := 0;
theta0 := 355/1000;
thetaL := 1/10;
L := 8/100;
mu := a*(theta0 + b)/d;
c := a*(thetaL + b)/d;

mu := a*(theta0 + b)/d;
c := a*(thetaL + b)/d;

V := 1/(2*Pi)*exp(-d*k^2*t)*((exp(k*x*I)(mu - k*I) - exp(-mu*L)*exp(k*(L - x)*I)*(mu + L*I))*k*cos(k*L)/(k^2 + mu^2) + c*sin(k*L) - exp(k*L*I)(k*I + c)*sin(k*x)*(1 - exp(-mu*L)*exp(-I*k*L))/(mu + k*I) - (k*cos(k(L - x)) + c*sin(k(L - x)))*(1 - exp(-mu*L)*exp(k*L*I))/(mu - k*I) + 2*I*k*d*(k*cos(k(L - x)) + c*sin(k(L - x)))/(d*k^2 + a*q/d))/(k*cos(k*L) + c*sin(k*L)):

l := 5;
k1 := r -> l + I + r*exp(1/6*I*Pi);
k2 := r -> -l + I + r*exp(5/6*I*Pi);
k3 := s -> s + I;

dk1 := D(k1);
dk2 := D(k2);
dk3 := D(k3);

integrand1 := Re(eval(V, k = k1(r))*dk1(r) + eval(V, k = k2(r))*dk2(r));
integrand3 := Re(eval(V, k = k3(s))*dk3(s));
integrand2 := simplify(evalc(integrand1));

integrand4 := simplify(evalc(integrand3));
approx_u := proc(x, t) local temp1, temp2; temp1 := Int(eval(integrand2, [:-x = x, :-t = t]), r = 0 .. infinity, method = _d01amc); temp2 := Int(eval(integrand4, [:-x = x, :-t = t]), s = -L .. L, method = _d01ajc); evalf(temp1 + temp2); end proc;

How to force change of units in ScatterPlot?

FDS_ERT — Mon, 13 Apr 2026 19:31:58 Z

Dear power users,

In the attached document, I try to have DO2i in units of "mL/min/m²" on the Y-axis of my plot. I have tried to obtain this with "convert", but to no avail. Could anyone show me how to obtain the desired result?

Thank you for your timePlotQuestionMaplePrimes.mw

Why is evaluation lacking in ExpressionTools:-Compare

C_R — Sat, 11 Apr 2026 18:14:12 Z

Can someone explain why the element selection inside Compare works differently for the second argument?

(1)

(2)

(3)

(4)

(5)

(6)

Download Compare_and_indexing_output.mw

How much will the meadow cost?

Alfred_F — Sat, 11 Apr 2026 09:38:10 Z

With thanks to @sand and @janhardo for their help in solving a variational problem using Maple, I'm presenting a puzzle worth remembering. It was originally published in an IBM competition over 20 years ago under simpler conditions than those presented here, and later posed in a more challenging form in private circles:

A farmer wants to buy a section of a large meadow/pasture for his sheep. He likes a lone, large oak tree on the meadow. This tree is to be the starting and ending point of the fence around the desired section. The fence is exactly 100 meters long. The farmer creates a sketch of the situation. He places the oak tree at the origin of a Cartesian coordinate system with a positive y-axis pointing north and sketches the estimated location of the desired meadow section east of the oak tree. The seller then stipulates that the price per square meter increases linearly eastward by a factor of 1/m³. An agreement is reached, and the farmer now considers the optimal route for the fence to maximize the return on his investment.

The fence route without corners and the value of the purchased meadow must be calculated.

A sphere with latitude and longitude circles

erik10 — Fri, 10 Apr 2026 22:00:48 Z

Dear Maple users

I can easily draw a sphere with the following command:

plot3d(1, t = -Pi .. Pi, p = 0 .. Pi, coords = spherical)

Let's say I want to change the number of latitude circles so that there is one for every 10 degrees? Longitude circles are given for every 15 degrees, which is appropriate - corresponding to one for every hour! But in general: Is there a way to change the number of circles of both types? Or maybe you need to piece together a plot of several kinds of plots?

Erik

Factorizing nested radicals

danielpf — Fri, 10 Apr 2026 16:21:44 Z

# The question is: how to get S knowing E? All the attemps below after S assigned (suggested by Claude) fail factoring E.

restart;

interface(showassumed = 0):
assume(a>=0, b>=0, c>=0);
assume(x::real, y::real,z::real);

S := sqrt(x^2+(a+sqrt(y^2+(b+sqrt(z^2+c^2))^2))^2):
E := expand(S):
simplify(E,sqrt):
combine(E,sqrt):
simplify(combine(E, sqrt), sqrt):
evalindets(E, 'radical', f -> simplify(f, sqrt)):
simplify(radnormal(E), sqrt):